purpose. To compare ocular component growth curves among four refractive error groups in children.

methods Cycloplegic refractive error was categorized into four groups: persistent emmetropia between −0.25 and +1.00 D (exclusive) in both the vertical and horizontal meridians on all study visits (*n* = 194); myopia of at least −0.75 D in both meridians on at least one visit (*n* = 247); persistent hyperopia of at least +1.00 D in both meridians on all visits (*n* = 43); and emmetropizing hyperopia of at least +1.00 D in both meridians on at least the first but not at all visits (*n* = 253). Subjects were seen for three visits or more between the ages of 6 and 14 years. Growth curves were modeled for the persistent emmetropes to describe the relation between age and the ocular components and were applied to the other three refractive error groups to determine significant differences.

results At baseline, eyes of myopes and persistent emmetropes differed in vitreous chamber depth, anterior chamber depth, axial length, and corneal power and produced growth curves that showed differences in the same ocular components. Persistent hyperopes were significantly different from persistent emmetropes in most components at baseline, whereas growth curve shapes were not significantly different, with the exception of anterior chamber depth (slower growth in persistent hyperopes compared with emmetropes) and axial length (lesser annual growth per year in persistent hyperopes compared with emmetropes). The growth curve shape for corneal power was different between the emmetropizing hyperopes and persistent emmetropes (increasing corneal power compared with decreasing power in emmetropes).

conclusions Comparisons of growth curves between persistent emmetropes and three other refractive error groups showed that there are many similarities in the growth patterns for both the emmetropizing and persistent hyperopes, whereas the differences in growth lie mainly between the emmetropes and myopes.

^{ 1 }Sperduto et al.

^{ 2 }estimated the prevalence of myopia in 12- to 17-year-olds in the United States in 1971 to 1972 to be 24%. Although many studies have been performed in the area of childhood myopia, there is limited information about the course and progression of myopia and accompanying changes in the ocular components over extended periods. Comparing the course of component development in emmetropes and children with refractive error provides a useful description of the natural history of ocular growth.

^{ 3 }

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }

^{ 10 }

^{ 11 }Although these studies have investigated the change in myopia with age, very few look at the accompanying changes in the ocular components.

^{ 4 }

^{ 7 }Later studies have concentrated primarily on axial length.

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 11 }

^{ 7 }presented the results from a randomized clinical trial evaluating the impact of bifocals with a +1.75 D add, compared with full correction with spectacles for distance vision only versus full correction with spectacles for continuous wear. Regression models of myopia progression over a 3-year period by gender were presented. In the spectacle-wearing group, myopic progression was faster in girls than in boys. The 60 slowest progressors were compared with the 60 fastest progressors on corneal power (both initial and final), final anterior chamber depth, final lens thickness, and final axial length. There were significantly more girls among the 60 fastest progressors. The only statistically significant difference between the two groups was in axial length, with the fastest progressors having an average axial length of 0.88 ± 0.76 mm longer than the slowest progressors.

^{ 7 }

^{ 6 }presented results of the Correction of Myopia Evaluation Trial evaluating single-vision versus progressive addition lenses in children on the progression of myopia. Over the 3 years of the study, the spherical equivalent progressed by approximately 1.4 D in the single-vision lens group. An increase in axial length of 0.75 mm over the same period showed a significant correlation with change in refractive error (

*r*= 0.89).

^{ 5 }conducted a single-vision versus bifocal lens myopia progression trial, enrolling only myopic children with near-point esophoria. Vitreous chamber depth increased approximately 0.48 mm after 30 months in the single-vision lens group, whereas axial length changed by 0.49 mm.

^{ 12 }

^{ 13 }Most data describe the frequency of hyperopia in a given sample.

^{ 14 }No studies discuss the ocular components, their growth, or their relationship to hyperopia in childhood.

^{ 15 }Whereas the number of myopes increased over the years, the number of hyperopes remained unchanged (mean change in the hyperopes: +0.04 ± 0.74 D). Mäntyjärvi

^{ 16 }found little change in 46 hyperopes studied (mean change: −0.12 ± 0.14 D/y). Hirsch

^{ 17 }examined children at age 5 or 6 years and then again at age 13 or 14 years. He found that all children who were +1.50 D or more hyperopic at age 5 or 6 years (

*n*= 33) and 88% of children who were between +1.25 and +1.49 D at age 5 or 6 (

*n*= 8) years remained hyperopic at age 13 or 14 years. These studies indicate that children with hyperopia are more likely to remain hyperopic. Ocular components have not been examined in hyperopes over time.

^{ 18 }Children were recruited from the Orinda Union School District in California to participate in a longitudinal study evaluating risk factors for myopia and the development of the associated ocular components. Individuals and their parents provided informed consent according to the tenets of the Declaration of Helsinki. Informed consent procedures and the study protocol were approved by the University of California, Berkeley’s Committee for the Protection of Human Subjects. Data presented herein were obtained from 1989 through 2001. To be included in these analyses, the subject had to have at least three visits between the ages of 6 to 14 years to allow for the generation of ocular component growth curves.

^{ 19 }This method treats each spherocylinder as a vector that can then be manipulated by standard linear algebra matrices to provide means and standard deviations of sphere, cylinder, and axis. Mean spherocylinders were also converted to horizontal and vertical meridian refractions.

^{ 20 }which is an updated version of still-flash photography comparison ophthalmophakometry

^{ 21 }

^{ 22 }that measures Purkinje images I, III, and IV formed close to the optic axis by a collimated light source, with digitized, computer analysis of multiple images. The child was seated behind the instrument with an eye patch on his or her left eye and instructed to fixate a red-light–emitting diode on a movable arm while the reflected Purkinje images I, III, and IV were recorded. Lens power was calculated with the Gullstrand-Emsley schematic eye indices of refraction for the aqueous and the vitreous (4/3) and the crystalline lens (1.416).

^{ 23 }An equivalent index and calculated lens power were also found with an iterative procedure that produces agreement between measured refractive error and that calculates by using ocular component data from ultrasound and Purkinje image data from phakometry.

^{ 24 }Mixed modeling is particularly powerful because it allows for the presence of a variable number of data points—that is, an otherwise eligible subject is not excluded for missing observations due to the potential for differing lengths of follow-up. Missing data are handled within the iterative maximum-likelihood procedure, in which all available subject data were used, even in the calculations. The maximum-likelihood procedure chooses the parameters that will maximize the likelihood of observing the given set of sample data.

^{ 25 }In short, each outcome was modeled as a linear function of several mathematical forms of age, which included natural log, quadratic, age,

^{ 2 }inverse(age), and inverse[natural log(age)] and assuming points of inflection. In these latter models, cut points based on age were included in the model to allow the shape of the curve to vary before and after a given cut point. The cut points were selected within 0.5-year increments from age 9 to 12 years, so that there was a sufficient number of data points both before and after the cut point and so that the cut point was within the age at which myopia might be expected to develop. Akaike’s information criterion (AIC) values from each model were used to determine which function of age and which variance–covariance structure best described the ocular component changes.

^{ 26 }The best model was considered to be the one with the lowest AIC value, and model effectiveness was assessed by the model χ

^{2}. The probability was used to assess the significance of model fit. Once the best-fitting model for emmetropes was determined, this functional form was applied to the data for the myopes and for both groups of hyperopes, to derive curves for those groups. Parameter estimates from each curve were then compared with corresponding parameters from the emmetropic model. Allowing each refractive group to have growth curves with their best-fitting functional form would prevent comparisons between curves because of the lack of a comparison method across models. By fixing the functional form as the optimal model for the emmetropes, we maintained the ability to compare the estimated curves among refractive error groups.

^{2}= 139.96,

*P*< 0.0001), with the persistent emmetropes more likely to have attended fewer visits than the myopes, the persistent hyperopes, or the hyperopes. Thirty-seven percent of the myopes, 42% of the emmetropizing hyperopes, and 33% of the persistent hyperopes had a full eight visits. Only 15% of the persistent emmetropes attended all eight visits. Mean years of follow-up (±SD) were 3.7 ± 1.9 for the persistent emmetropes, 5.0 ± 2.0 for the myopes, 5.4 ± 1.7 for the emmetropizing hyperopes, and 4.6 ± 2.1 years for the persistent hyperopes (analysis of variance,

*P*< 0.0001). Post hoc comparisons show that the persistent emmetropes had a significantly shorter follow-up period than did the myopes (

*P*= 0.0023), the emmetropizing hyperopes (

*P*< 0.0001), and the persistent hyperopes (

*P*< 0.0001). There was also a marginally significant difference between the follow-up period of emmetropizing hyperopes and persistent hyperopes (

*P*= 0.046). The visits for all subjects were overwhelmingly consecutive—that in, a subject who had three visits had three consecutive visits over a 2-year period, not visits spaced out over many years.

^{ 6 }(COMET Study) and Fulk et al.

^{ 5 }show increases in vitreous chamber depth and axial length in myopes, similar to our myopia curves. The COMET Study also shows similar results in increases in anterior chamber depth. Likewise, there is no change in the corneal radii component from COMET. Over the course of 3 years, there was 0.03-mm change in corneal radii.

^{ 6 }Our myopia curves show little change in corneal power as well. The one component that seems to be on a different path is lens thickness. The COMET Study shows a mean change in lens thickness over 3 years in the single vision lens group of −0.01 mm. In our study, over a similar age range of 6 to 11 years, there appeared to be a decrease in lens thickness of approximately 0.14 mm before a leveling off. A potential reason for this is that our myopic subjects were a combination of pre- and post-onset myopes. The COMET subjects were always myopic. Lens thickness should be studied in more detail before and after the onset of myopia.

^{ 25 }were applied to each of the components within each of the refractive error groups—that is, a total of 48 models for each refractive error group–component pair. Just as for the persistent emmetropic group, AIC values were used to determine the most appropriate model to relate age and each ocular component within each refractive error group. In several cases, the persistent emmetropic model represented the best model for a refractive error group or component (two models in myopes and one model in emmetropizing hyperopes). For the remaining components, the AIC corresponding to the persistent emmetropic model was often relatively close (within 10%) to the AIC of the best model. There were three cases in which the persistent emmetropic form AIC and the best model differed by more than 10%, which infers that the persistent emmetrope model was not a good fit for that data (models not shown). Therefore, even after forcing the persistent emmetropes’ models on other refractive groups, the models seem to make an accurate representation of change in an ocular component with age.

**Figure 1.**

**Figure 1.**

Racial/Ethnic Group | Myopes n (%) | Emmetropes n (%) | Emmetropizing Hyperopes n (%) | Persistent Hyperopes n (%) |
---|---|---|---|---|

American Indian | 1 (50.0) | 0 | 1 (50.0) | 0 |

Asian | 59 (72.0) | 16 (21.1) | 6 (2.4) | 1 (1.2) |

African American | 1 (33.3) | 1 (33.3) | 1 (33.3) | 0 |

Hispanic | 4 (26.7) | 7 (46.7) | 2 (13.3) | 2 (13.3) |

White | 178 (28.4) | 170 (27.1) | 240 (38.3) | 39 (6.2) |

Other | 4 (50.0) | 0 | 3 (37.5) | 1 (12.5) |

Number of Visits | Myopes n (%) | Emmetropes n (%) | Emmetropizing Hyperopes n (%) | Persistent Hyperopes n (%) |
---|---|---|---|---|

3 | 59 (23.9) | 96 (49.5) | 21 (8.3) | 12 (27.9) |

4 | 11 (4.5) | 14 (7.2) | 28 (11.1) | 5 (11.6) |

5 | 15 (6.1) | 7 (3.6) | 29 (11.4) | 3 (7.0) |

6 | 45 (18.2) | 45 (23.2) | 42 (16.6) | 8 (18.6) |

7 | 25 (10.1) | 3 (1.5) | 26 (10.3) | 1 (2.3) |

At least 8 | 92 (37.2) | 29 (15.0) | 107 (42.3) | 14 (32.6) |

Variable | Myopes | Emmetropes | Emmetropizing Hyperopes | Persistent Hyperopes |
---|---|---|---|---|

Spherical equivalent (D) | −0.49 ± 1.38 | 0.54 ± 0.22 | 1.36 ± 0.48 | 2.45 ± 0.92 |

Age (y) | 7.98 ± 2.1^{*} | 9.40 ± 2.3 | 7.06 ± 1.3^{, †} | 7.94 ± 2.1^{, ‡} |

Lens refractive index | 1.430 ± 0.01 | 1.429 ± 0.01 | 1.432 ± 0.01 | 1.434 ± 0.01^{, ‡} |

Gullstrand lens power (D) | 20.79 ± 1.5 | 20.62 ± 1.4 | 21.18 ± 1.3 | 21.26 ± 1.8 |

Calculated lens power (D) | 23.94 ± 2.2 | 23.63 ± 2.0 | 24.98 ± 2.0 | 25.58 ± 2.5^{, ‡} |

Lens thickness (mm) | 3.50 ± 0.2 | 3.47 ± 0.1 | 3.54 ± 0.2 | 3.55 ± 0.2 |

Anterior chamber depth (mm) | 3.68 ± 0.2 | 3.69 ± 0.2 | 3.53 ± 0.2^{, †} | 3.44 ± 0.3^{, ‡} |

Axial length (mm) | 23.05 ± 0.9^{*} | 22.93 ± 0.7 | 22.30 ± 0.6^{, †} | 21.91 ± 0.9^{, ‡} |

Vitreous chamber depth (mm) | 15.87 ± 0.9^{*} | 15.77 ± 0.7 | 15.24 ± 0.6 | 14.93 ± 0.8^{, ‡} |

Corneal power (D) | 44.30 ± 1.4^{*} | 43.61 ± 1.5 | 43.79 ± 1.3 | 43.54 ± 1.5 |

**Figure 2.**

**Figure 2.**

Ocular Component | Models | P |
---|---|---|

Crystalline lens index | E: 1.427 + 0.162 · age^{−2} | |

PH: 1.429 + 0.222 · age^{−2} | 0.4645 | |

M: 1.428 + 0.079 · age^{−2} | 0.2563 | |

EH: 1.429 + 0.121 · age^{−2} | 0.6064 | |

Gullstrand lens power | E: Age ≤ 9 years 27.001 − 2.983 · ln(age) | |

Age > 9 years 25.080 − 2.057 · ln(age) | ||

PH: Age ≤ 9 years 26.399 − 2.522 · ln(age) | ||

Age > 9 years 24.408 − 1.654 · ln(age) | 0.6376 | |

M: Age ≤ 9 years 28.775 − 3.948 · ln(age) | ||

Age > 9 years 24.311 − 1.945 · ln(age) | 0.0608 | |

EH: Age ≤ 9 years 25.834 − 2.399 · ln(age) | ||

Age > 9 years 24.633 − 1.888 · ln(age) | 0.3166 | |

Calculated lens power | E: 21.850 + 133.590 · age^{−2} | |

PH: 22.501 + 158.168 · age^{−2} | 0.2369 | |

M: 21.244 + 149.618 · age^{−2} | 0.1972 | |

EH: 22.251 + 129.020 · age^{−2} | 0.7366 | |

Lens thickness | E: Age ≤ 9.5 years 3.799 − 0.041 · age | |

Age > 9.5 years 3.352 + 0.006 · age | ||

PH: Age ≤ 9.5 years 3.746 − 0.026 · age | ||

Age > 9.5 years 3.428 + 0.007 · age | 0.0954 | |

M: Age ≤ 9.5 years 3.841 − 0.046 · age | ||

Age > 9.5 years 3.389 + 0.002 · age | 0.1827 | |

EH: Age ≤ 9.5 years 3.778 − 0.036 · age | ||

Age > 9.5 years 3.363 + 0.007 · age | 0.5221 | |

Anterior chamber depth | E: 1.817 − 0.265 · ln(age)^{2} + 1.441 · ln(age) | |

PH: 2.773 − 0.062 · ln(age)^{2} + 0.447 · ln(age) | 0.0048 | |

M: 1.425 − 0.311 · ln(age)^{2} + 1.749 · ln(age) | <0.0001 | |

EH: 1.381 − 0.349 · ln(age)^{2} + 1.787 · ln(age) | 0.1054 | |

Axial length | E: Age ≤ 10.5 years 20.189 + 1.258 · ln(age) | |

Age > 10.5 years 21.353 + 0.759 · ln(age) | ||

PH: Age ≤ 10.5 years 19.926 + 0.970 · ln(age) | ||

Age > 10.5 years 19.825 + 1.010 · ln(age) | 0.0273 | |

M: Age ≤ 10.5 years 18.144 + 2.391 · ln(age) | ||

Age > 10.5 years 17.808 + 2.560 · ln(age) | <0.0001 | |

EH: Age ≤ 10.5 years 19.660 + 1.366 · ln(age) | ||

Age > 10.5 years 21.180 + 0.715 · ln(age) | 0.2231 | |

Vitreous chamber depth | E: Age ≤ 10 years 13.154 + 1.211 · ln(age) | |

Age > 10 years 14.754 + 0.513 · ln(age) | ||

PH: Age ≤ 10 years 12.860 + 1.014 · ln(age) | ||

Age > 10 years 13.437 + 0.762 · ln(age) | 0.0743 | |

M: Age ≤ 10 years 11.297 + 2.228 · ln(age) | ||

Age > 10 years 10.907 + 2.416 · ln(age) | < 0.0001 | |

EH: Age ≤ 10 years 12.708 + 1.308 · ln(age) | ||

Age > 10 years 14.339 + 0.606 · ln(age) | 0.3867 | |

Corneal power | E: 42.131 − 0.566 · ln(age)^{2} + 2.033 · ln(age) | |

PH: 45.061 + 0.161 · ln(age)^{2} − 1.033 · ln(age) | 0.4073 | |

M: 44.253 − 0.009 · ln · (age)^{2} + 0.008 · ln(age) | 0.0009 | |

EH: 44.525 + 0.163 · ln(age)^{2} − 0.704 · ln(age) | <0.0001 |

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**

**Figure 8.**

**Figure 8.**

**Figure 9.**

**Figure 9.**

**Figure 10.**

**Figure 10.**

*Optics of Vision*; vol. 1.